Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 1 - First-Order Differential Equations - 1.2 Basic Ideas and Terminology - Problems: 29

Answer

$y' = \frac{(1 - y^{2})}{2(xy + 1)}$

Work Step by Step

$xy^{2} + 2y - x = c$ Implicit differentiation: differentiating the equation in terms of $x$ $2xyy' + y^{2} + 2y' - 1 = 0$ Express the formula in terms of $y'$: $y' = \frac{(1 - y^{2})}{2(xy + 1)}$
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